Arrange onion slices in a single layer in a 13- x 9-inch baking dish.
Stir together vinegar and next 4 ingredients. Pour over onion slices. Cover and chill 8 hours, turning once.
Remove onions from dressing with a slotted spatula, reserving dressing.
Grill onion slices, covered with grill lid, over medium-high heat (350° to 400°) 2 minutes on each side or until crisp-tender and golden.
Layer half of grilled onion slices each with 1 cheese round, 2 basil leaves, and 1 tomato slice; top with remaining half of onion slices.
Grill onion stacks, covered with grill lid, over medium-high heat 3 minutes or until cheese melts. Serve onion stacks with reserved dressing. Garnish, if desired.
So tasty! Make sure you see the cheese melting before you take it off the grill. Excellent!
Only one minor change - we grilled portobellas and served everything inside of them. Excellent!
